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Cluster synchronization of Markovian switching complex networks with hybrid couplings and stochastic perturbations

Author

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  • Liu, Quan
  • Kan, Bao
  • Wang, Qiang
  • Fang, Yilin

Abstract

In this work, we extend cluster synchronization into a more general complex network model, a class of Markovian switching complex networks composed of nonidentical nodes with hybrid couplings. These networks are also influenced by coupling delays and disturbed by stochastic noise perturbations. Based on some definitions, assumptions and lemmas, an adaptive controller is designed. Particularly, by constructing a novel stochastic Lyapunov–Krasovskii function and employing the linear matrix inequalities (LMIs), Ito’s formula and the stochastic Lasalle-type invariance theorem, the effectiveness of the designed controller is proved. Besides, a numerical example is illustrated for further verifications and conclusions.

Suggested Citation

  • Liu, Quan & Kan, Bao & Wang, Qiang & Fang, Yilin, 2019. "Cluster synchronization of Markovian switching complex networks with hybrid couplings and stochastic perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    • Handle: RePEc:eee:phsmap:v:526:y:2019:i:c:s0378437119305618
    DOI: 10.1016/j.physa.2019.04.173
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